At the time, police said there was no evidence of "any form of assault".

Police have said his body may have been there for a week and investigations are ongoing.

His mother and sister flew out of Hobart yesterday, asking if things may have been different if their son and brother had received the care they say he sought for his mental health condition at Royal Hobart Hospital in the weeks leading up to his death.

"He had everything he needed. He had a car, he had a unit, he had a community that are really mourning him. He just needed that help. Desperately," Kay Lyons, Matthew's mother, said.

"He was quite desperate for help. And he didn't get it."

The Health Department has issued a statement saying it was not appropriate to comment on individual patient's care while investigations are continuing.

"At this point in time, a cause of death, or any factors leading to that man's death have not been formally determined," the department said in a statement.

Matthew 'came from loving family'

In the weeks leading up to his death, Matthew's condition had worsened, according to his sister Cassandra.

His family said they travelled to see him in September because they were worried about his health and whether he could access care in an emergency.

His sister said she had also called to try to get help from Tasmania's health services.

"I was saying, 'I'm his sister, I want you to pay attention that he needs assistance, he needs help to get into emergency. Is there something I can do or say to help him get in'?" she said.

The family have met with his psychiatrist and case worker in the days since his death, and say they are not angry at them. Kay has said she doesn't tend to get angry. She is frustrated.

"We feel this may not have happened if Matthew was in hospital at this time," she said.

The family said Matthew was "not homeless and came from a very loving family" and reports suggesting otherwise were wrong and had caused "great pain to the people that lived with him, loved him and were his friends".

"He came to Tasmania for a more peaceful life," they wrote in their letter.

"As he suffered from some mental health challenges, the slower pace and climate helped him.

"He became a big part of the community down here and was well-liked and valued by all around him, both residents and staff."

Cooking at Salvation Army 'gave Matthew a purpose'

Many of those who knew Matthew live only 300 metres away from where he was found, at his home of three years, a complex of 50 units managed by the residents and the Salvation Army.

A number of the residents live with mental health challenges. They know the health system and the stress it's under for people seeking help.

"There's a genuine sadness and frustration and I guess even anger. And that's not just shared by me. That's shared by the entire tenant community here. I think I speak on behalf of the staff as well," Ant Fagan, program manager at Salvation Army Housing in Campbell Street in Hobart, said.

Mr Fagan said Matthew was a valued resident in the community in Campbell Street.

"He was a cook, he took on a role to make meals for everybody in the community on a weekly basis," Mr Fagan said.

Many of the ingredients used by Matthew came from the community garden in the large apartment courtyard, with his fellow residents remembering him cooking to music, the aromas filling the area as he worked up his weekly batch.

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Mr Fagan said supportive housing services like the one in Campbell Street were increasingly being leaned on by the health system as it sought to discharge patients to free up beds.

Those with somewhere, anywhere, to go are being released first.

"More and more social housing providers are being asked to provide services that are beyond their remit, to step into areas that aren't necessarily their expertise or where they have training," he said.

"Sometimes that's not always what the person needs."

Matthew's family have taken his ashes with them.

"Rest in peace Matthew, you will always be loved and remembered," the last line of their letter reads.

Department of Health secretary Mike Pervan released a statement earlier which read in full:

"Firstly, on behalf of the Department of Health and the Tasmanian Health Service, I offer my deepest condolences to Mr Lyons' family. I can only imagine the emotions they are experiencing at this time of their grief.

"It would be entirely inappropriate for me to provide details of an individual patient's care, particularly in a situation where matters remain under investigation by Tasmania Police.

"It is concerning that the ABC would choose to broadcast such information despite knowing that an investigation is continuing, and therefore, conclusions have not been determined.

"The THS is not aware of any adverse events relating to Mr Lyons while he was under its care."